Assessing and Characterizing Climate Vulnerabilities in Agriculture-Based Livelihoods: South Sulawesi

1 Introduction

Abstrak

Penghidupan berbasis pertanian kini makin rentan terhadap perubahan iklim, tetapi informasi mengenai potensi resiko dan kebutuhan adaptasi mereka masih sangat terbatas. Bahan ajar ini disusun untuk mengisi kekosongan ini dengan mengevaluasi berbagai jenis kerentanan yang mempengaruhi mata pencaharian berbasis pertanian di tingkat provinsi. Kami melakukan penilaian kerentanan untuk mengidentifikasi risiko utama serta akar penyebabnya, dan potensi adaptasi, dengan fokus pada peningkatan taraf hidup, keberlanjutan produksi komoditas-komoditas kunci, dan pengelolaan lahan secara menyeluruh.

Mengingat keanekaragaman kondisi di masing-masing provinsi, kami memfokuskan perhatian pada kecamatan-kecamatan dengan fitur biofisik dan sosial-ekonomi yang mirip. Ini membantu kami mempermudah tugas dalam mengidentifikasi risiko yang identik antar kecamatan. Kami mendefinisikan area-area homogen ini, atau ‘tipologi,’ dengan menggunakan pengelompokan K-means. Pengelompokan ini didasarkan pada komposit dari indikator biofisik dan sosial-ekonomi. Untuk mempermudah proses pengelompokan, kami menggunakan analisis PCA untuk menyederhanakan dimensi data.

Abstract

Smallholder farmers are increasingly vulnerable to climate change, yet little is known about their specific risks and adaptation requirements. Our study aims to address this gap by examining the different vulnerabilities affecting agriculture-based livelihoods at the provincial level. We conducted climate vulnerability assessments to identify key risks and their root causes, as well as possible mitigation measures, with a focus on sustaining livelihoods, key commodities production, and overall land management.

Considering the diverse conditions of the study area, we narrowed our focus to locations with similar biop hysical and socio-economic features. This helped us streamline the task of spotting common risks across communities. We defined these homogeneous areas, or ‘typologies,’ using K-means clustering. The clustering was based on a composite of biophysical and socio-economic indicators. To make the clustering process more precise, we applied PCA analyses to simplify the data dimensions.

Objective

We aimed to identify homogeneous areas, or ‘typologies’, with similar biophysical and socio-economic features across South Sulawesi Province, using K-means clustering on PCA-simplified data to infer common risks across communities.

2 Study area & Data

Study area

The South Sulawesi province, located in the southern peninsula of Sulawesi, Indonesia, spans an area of 46,717 square kilometres. The province is characterised by a north-south chain of mountains, topped by volcanic cones and bisected midway by the Tempe Lake valley. The climate is characterised by high rainfall throughout the year, typical of tropical rainforest climates.

South Sulawesi is home to a population of approximately 8.851 million people as of 2019. The province is characterised by a moderate level of income inequality, as reflected in the Gini ratios for its districts, which ranged from around 0.32 to 0.40 in 2022. The province scored 7.22 on the Human Development Index in 2022.

The Gross Domestic Product (GDP) of South Sulawesi was approximately 605.145 billion Indonesian Rupiah in 2022, which is equivalent to around 4,075 million US dollars. This places South Sulawesi as the 9th largest economy among the provinces in Indonesia.

Agriculture plays a significant role in the province’s economy, with an estimated one million farmers operating in South Sulawesi, according to the 2018 Survei Pertanian Antar Sensus (SUTAS) conducted by the Badan Pusat Statistik (BPS). Major agricultural products include rice, corn (maize), copra (dried coconut meat), coffee, spices, vegetable oil, sugarcane, soybeans, and sweet potatoes. The forests of the region yield valuable resources such as teak and rattan, and deep-sea fishing also contributes to the local economy.

Data Collection

Understanding the vulnerability of smallholder farmers to climate change involves examining a variety of biophysical and socio-economic factors. These factors, represented as grid layers or proxies, are chosen based on literature reviews, field observations, and expert insights. However, not all potential variables are readily available or of sufficient quality for analysis.

These factors are organised into five categories, known as livelihood capitals: natural, physical, human, social, and financial. Each represents a unique aspect that can influence a farmer’s vulnerability to climate change.

• Natural capital includes essential natural resources like forests, rivers, and arable land, as well as climate factors such as temperature and precipitation.

• Physical capital refers to infrastructure and production resources, including proximity to plantations, roads, and processing facilities.

• Human capital encompasses the population’s knowledge, skills, and health, reflected in variables like village population and unemployment rate.

• Social capital represents the social networks that provide support and resources to farmers, indicated by factors like the percentage of smallholder agricultural areas in a village.

• Financial capital involves financial resources, income diversity, and access to credit, represented by variables such as farm size and crop yield.

Vulnerability indicators with descriptions and data sources

No	Data	Source	Unit	Category	Low Pixel Value~ Vulnerable?	High Pixel Value ~ Vulnerable?	Assumption	Correlation with Vulnerability	Livelihood Capitals
1	Distance to plantation	Peta Tutupan Lahan 2017 from KLHK	m	Distance to infrastructure	No	Yes	The closer to the plantation, the easier the access to capital	+	Physical Capital (P)
2	Distance to highway	Peta Tutupan Lahan 2017 from KLHK	m	Distance to infrastructure	No	Yes	The closer to the road, the easier the access to capital	+	Physical Capital (P)
4	Distance to commodity processing factory	ICRAF	m	Distance to infrastructure	No	Yes	The closer to the factory, the easier the access to markets and processing facilities	+	Physical Capital (P)
5	Distance to plantation concession	Dinas Perkebunan Provinsi Kalimantan Barat	m	Distance to infrastructure	No	Yes	The closer to the concession, the easier the access to plantation resources	+	Physical Capital (P)
6	Distance to forest	Peta Tutupan Lahan 2017 from KLHK	m	Distance to natural resources	No	Yes	More diverse alternative livelihoods, maintains good hydrological cycle	+	Natural Capital (N)
7	Distance to river	BIG	m	Distance to natural resources	No	Yes	Distance to river facilitates access to clean water and irrigation, as well as transportation	+	Natural Capital (N)
8	Distance to mining area	BIG	m	Distance to natural resources	No	Yes	The closer to the mining area, the easier the access to mineral resources and potential job opportunities	+	Natural Capital (N)
9	Distance to burned area	KLHK 2015	m	Distance to natural disaster (fire)	Yes	No	The closer to the fire, the more impacted	-	Natural Capital (N)
10	Percentage of agricultural area (small holder) in the village	Peta Tutupan Lahan 2017 from KLHK	%	Land use and land cover	Yes	No	The higher the percentage, the higher the access to small-scale agriculture	-	Natural Capital (N)
11	Percentage of plantation area per village	Peta Tutupan Lahan 2017 from KLHK	%	Land use and land cover	No	Yes	The higher the percentage, the higher the dependence on palm oil industry	+	Financial Capital (F)
12	Percentage of forested area in the village	Peta Tutupan Lahan 2017 from KLHK	%	Land use and land cover	Yes	No	More diverse alternative livelihoods, maintains good hydrological cycle	-	Natural Capital (N)
13	Percentage of shrubland in the village	Peta Tutupan Lahan 2017 from KLHK	%	Land use and land cover	No	Yes	Shrubland is not good enough for the water cycle	+	Natural Capital (N)
14	Percentage of forested area at the regency level	Peta Tutupan Lahan 2017 from KLHK	%	Land use and land cover	Yes	No	More diverse alternative livelihoods, maintains good hydrological cycle	-	Natural Capital (N)
15	Percentage of plantation at the regency level	Peta Tutupan Lahan 2017 from KLHK	%	Land use and land cover	No	Yes	The higher the percentage, the higher the dependence on palm oil industry	+	Financial Capital (F)
16	Percentage of water area compared to regency area	BIG	%	Land use and land cover	No	Yes	The higher the percentage, the easier the access to water resources	-	Natural Capital (N)
17	Distance to deforestation	Peta Tutupan Lahan 2017 from KLHK	m	Land use and land cover	Yes	No	The closer to deforestation, the more impacted	-	Natural Capital (N)
18	Deforestation area size	Peta Tutupan Lahan 2017 from KLHK	km_	Land use and land cover	Yes	No	The larger the deforestation area, the more impacted	-	Natural Capital (N)
19	Flood occurrence	Potensi desa BPS 2018	events/year	Natural disaster	Yes	No	The more frequent the flood, the more impacted	+	Natural Capital (N)
20	Flash flood occurrence	Potensi desa BPS 2018	events/year	Natural disaster	Yes	No	The more frequent the flash flood, the more impacted	+	Natural Capital (N)
21	Fire occurrence	Potensi desa BPS 2018	events/year	Natural disaster	Yes	No	The more frequent the fire, the more impacted	+	Natural Capital (N)
22	Long drought occurrence	Potensi desa BPS 2018	events/year	Natural disaster	Yes	No	The more frequent the long drought, the more impacted	+	Natural Capital (N)
23	Village population	Potensi desa BPS 2018	people	Demography	No	Yes	The larger the population, the more potential for human impact	+	Human Capital (H)
24	Annual Temperature (?C)	WORLDCLIM 2.1	?C	Climate	No	Yes	The higher the temperature, the more potential for heat stress	+	Natural Capital (N)
25	Precipitation change	WORLDCLIM 2.1	mm/year	Climate	Yes	No	The greater the change in precipitation, the more potential for water stress	+	Natural Capital (N)
26	Arable land (%)	?	%	Agriculture	No	Yes	The higher the percentage of arable land, the more potential for agricultural production	-	Natural Capital (N)
27	Erosion risk (t ha_1 yr_1)	RUSLE	t ha_1 yr_1	Natural disaster	Yes	No	The higher the erosion risk, the more potential for land degradation	+	Natural Capital (N)
31	Unemployment rate (%)	BPS	%	Demography	Yes	No	The higher the unemployment rate, the more potential for economic stress	+	Human Capital (H)
32	Farm holdings smaller than 2 ha (%)	BPS	%	Access to land	No	Yes	The higher the percentage of small farms, the more potential for economic stress	+	Financial Capital (F)
33	Irrigated land (%)	?	%	Agriculture	No	Yes	The higher the percentage of irrigated land, the more potential for agricultural production	-	Natural Capital (N)
34	Mean yield of major crops (kg ha_1)	BPS	kg ha_1	Agriculture	No	Yes	The higher the yield, the more potential for agricultural production	-	Financial Capital (F)
35	Climate driven changes in major crop suitability	ECOCROP	% change	Agriculture	Yes	No	The greater the climate-driven changes, the more potential for crop stress	+	Natural Capital (N)
36	Poverty rate	BPS	%	Agriculture	Yes	No	The higher the poverty rate, the more potential for economic stress	+	Financial Capital (F)
37	Aridity index	WORLDCLIM 2.1	index value	Climate	Yes	No	The higher the aridity index, the more potential for water stress	+	Natural Capital (N)
38	Distance to market (Pasar Tradisional, Pusat Perbelanjaan,Toko Swalayan)	Direktori Pasar Indonesia 2020 BPS	m	Distance to infrastructure	No	Yes	The closer to the market, the easier the access to capital	+	Physical Capital (P)

2.1 Pipeline

A flowchart includes steps in performing PCA.

2.2 Loading the data

Reading the Data: We have an Excel file with lots of information. Each row in the file gives us details about a village, and the columns tell us about different factors that might make the village more or less vulnerable to climate change. There’s also a special sheet in the Excel file that explains what all these factors mean, their unique IDs, and how they’re measured.

2.2.1 The main dataset raw_df

Code

library(readxl)
library(corrplot)
library(caret)
library(gtExtras)
library(naniar)
library(knitr)

df_raw <-
  read_xlsx("data/analisa_tipologi_sulsel.xlsx",
            sheet = "fin_copas") |> 
  janitor::clean_names() |> dplyr::select(-c(idkec_2, idkec_3)) |> 
  mutate(across(-c(idkec_dum, sumber, nmprov, nmkab, nmkec), as.numeric))

Code

# Select a subset of columns for clarity
df_selected <- df_raw|>
  dplyr::select(1,7,8,10,11, 12) |> head()

# Create the table using gt
df_selected|>
  gt()|>
  tab_header(
    title = "A sample of the Data"
  )|>
  cols_label(
    idkec_dum = "ID",
    nmkab = "District",
    nmkec = "Sub-district",
    distance_to_plantation = "Dist. to Plantation (m)",
    distance_to_road = "Dist. to Road (m)",
    distance_to_commodity_processing_factory = "Dist. to Comm.Proc Factory (m)"
  )|>
  fmt_number(
    columns = c(distance_to_plantation, distance_to_road, distance_to_commodity_processing_factory),
    decimals = 2
  )

A sample of the Data
ID	District	Sub-district	Dist. to Plantation (m)	Dist. to Road (m)	Dist. to Comm.Proc Factory (m)
7301010a	KEPULAUAN SELAYAR	PASIMARANNU	221,140.99	3,151.66	295,618.47
7301011a	KEPULAUAN SELAYAR	PASILAMBENA	268,465.24	1,996.38	355,496.81
7301020a	KEPULAUAN SELAYAR	PASIMASSUNGGU	184,133.49	1,649.59	251,716.26
7301021a	KEPULAUAN SELAYAR	TAKABONERATE	163,497.97	4,252.98	242,261.12
7301022a	KEPULAUAN SELAYAR	PASIMASSUNGGU TIMUR	188,167.82	861.54	258,492.26
7301030a	KEPULAUAN SELAYAR	BONTOSIKUYU	99,706.86	744.58	173,876.77

Now we have a big table called df_raw. This table contains information like the name of the province, district, sub-district, and village. It also includes data about the village’s area, population density, and lots of other numerical factors. We then standardized the selected features/predictors to unit variance and zero mean and combined them into one layer.

Code

# Remove unnecessary columns from the original dataframe 'df_raw'
# The 'dplyr::select()' function is used to exclude these columns
df_gt <- df_raw |> 
  dplyr::select(-c(idkec_dum, kdprov, sumber, nmprov, nmkab, nmkec, periode, kdkab, kdkec, prec_change))

df_col_unstandardise <- df_raw |> dplyr::select(prec_change)

# Add a small constant (0.001) to every value in 'df_gt'
# This is often done to allow for log transformations of data that includes zeros
df_gt_plus <- df_gt + 0.001



# Log-transform and scale the data
# 1. 'as_tibble()' converts the dataframe to a tibble for easier manipulation
# 2. 'mutate_all(.funs = log10)' applies the base-10 logarithm to all columns
# 3. 'scale()' standardizes each column so that it has mean=0 and sd=1
scaled_df <-
  df_gt_plus |> as_tibble() |> mutate_all(.funs = log10) |> bind_cols(df_col_unstandardise) |>  scale(center = TRUE, scale = TRUE)

# Add back the columns that were removed earlier to create a complete, scaled dataframe
# 'bind_cols()' binds the selected columns from 'df_raw' and the scaled columns from 'scaled_df'
scaled_df_complete <- df_raw |> 
  dplyr::select(c(idkec_dum, kdprov, sumber, nmprov, nmkab, nmkec, periode, kdkab, kdkec)) |>  
  bind_cols(scaled_df)

# Remove the column 'korban_jiwa_kebakaran_hutan_dan_lahan_2018_2019' from the complete, scaled dataframe
scaled_df_complete_temp <- scaled_df_complete |> 
  dplyr::select(-korban_jiwa_kebakaran_hutan_dan_lahan_2018_2019)

3 Preparing the data

Before diving into the PCA, let’s ensure that the data meets the necessary requirements.

3.1 Check for missing values

Code

# Check for missing values
missing_data <- sapply(scaled_df_complete_temp, function(x) sum(is.na(x)))

# print missing data\
scaled_df_complete_temp|> filter_all(any_vars(is.na(.))) |>   dplyr::select("ID Kecamatan" = 1, "Nama Kabupaten" = 5, "Nama Kecamatan " = 6) |> kable(caption = "Kecamatan dengan data tidak lengkap")

Kecamatan dengan data tidak lengkap

ID Kecamatan	Nama Kabupaten	Nama Kecamatan
7313000a	WAJO	WAJO
7322011a	LUWU UTARA	SABBANG SELATAN
7322021a	LUWU UTARA	BAEBUNTA SELATAN
7322041a	LUWU UTARA	SUKAMAJU SELATAN
7325000a	LUWU TIMUR	LUWU TIMUR
7371081a	MAKASSAR	KEPULAUAN SANGKARRANG

Code

#remove missing data
scaled_df_complete_temp <- scaled_df_complete_temp[complete.cases(scaled_df_complete_temp), ]

3.2 Exclude identifiers

Code

df_pre_pca <- scaled_df_complete_temp |> 
  select(-c(idkec_dum, sumber, kdprov, nmprov, nmkab, nmkec, periode, kdkab, kdkec))

df_pre_pca |> kbl(caption = "Input data for a PCA Analysis") |>   kable_paper()|>
  scroll_box(width = "1000px", height = "500px")

Input data for a PCA Analysis

distance_to_plantation	distance_to_road	distance_to_commodity_processing_factory	distance_to_plantation_concession	distance_to_forest	distance_to_river	distance_to_burned_area	percentage_of_agricultural_area_small_holder_in_the_village	percentage_of_plantation_area_per_sub_district	percentage_of_forested_area_in_the_sub_district	percentage_of_shrubland_in_the_sub_district	percentage_of_water_area_compared_to_sub_district_area	distance_to_deforestation	percentage_deforestation_area_size	arable_land_percent	erosion_risk_t_ha_1_yr_1	indeks_bahaya_banjir	indeks_bahaya_longsor	buffer_to_500m_irigated_land	aridity_index	total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	rasio_elektrifikasi	rasio_sekolah_tinggi_sma_sederajat	rasio_pt	rasio_rs	rasio_faskes_1	rasio_pasar	rasio_minimarket_swalayan	banyak_kejadian_tanah_longsor_2018_2019	korban_jiwa_tanah_longsor_2018_2019	banyak_kejadian_banjir_2018_2019	korban_jiwa_banjir_2018_2019	banyak_kejadian_banjir_bandang_2018_2019	korban_jiwa_banjir_bandang_2018_2019	banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	banyak_kejadian_kekeringan_lahan_2018_2019	korban_jiwa_kekeringan_lahan_2018_2019	jumlah_sistem_peringatan_dini_bencana_alam	persentase_sistem_peringatan_dini_bencana_alam	rasio_embung_di_kecamatan	rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	annual_mean_temp	temp_change	annual_mean_prec	rasio_40pers_ekon_rendah_rt	rasio_40pers_ekon_rendah_indv	prec_change
2.6922633	1.7166810	2.0357668	-4.3825590	-0.6076871	2.7117976	3.3492440	-2.0718191	-1.0500575	1.3812193	-0.2416110	-0.1655192	-0.8987080	1.4974779	0.0159813	-1.3634738	0.0658418	0.0690122	-0.7093641	-2.8351594	-0.8784002	0.3900809	-0.8662722	-0.5335278	-0.4631427	-0.9351701	16.7717433	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	-0.8396838	-1.2024273	1.1710368	-0.9072150	-0.9131378	0.1837850	0.0129179	-0.1064804	-0.2500750	-1.0432363	0.1491026
2.9183618	1.2690894	2.2307442	-4.3825590	0.3766393	3.9039885	3.5942067	-0.3934067	-0.7356651	-0.3764903	-0.2416110	-0.1655192	0.1012585	0.3936954	0.5254928	-1.0656104	-2.0115443	0.0794378	-0.7093641	-4.2911316	-1.5251892	-0.3590277	-0.3356609	-0.5335278	-0.4631427	-1.0861552	0.5143758	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	-1.1001485	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1859142	0.0214586	-0.1515203	1.1414194	0.9709774	0.1881462
2.4787354	1.0820430	1.8658209	-4.3825590	-1.1584093	1.7751776	3.1240451	-2.9534347	-1.2100183	1.3370173	-0.2416110	-0.1655192	-1.6426342	1.9354174	-0.0945629	-0.9964380	-0.5942738	0.5340932	-0.7093641	-2.3585071	-1.3525855	0.4722171	-0.4940463	-0.5335278	-0.4631427	-0.9692783	0.2031787	0.6897151	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	-1.1638023	0.5072149	1.2216349	-0.9072150	-0.9131378	0.1772192	0.0014243	-0.0865877	0.8205483	0.6070416	0.0998882
2.3401524	2.0104617	1.8253486	-4.3825590	1.9776268	2.6743789	3.0626712	-3.1684987	0.8594398	-1.1028887	-0.2416110	-0.1655192	2.2341680	-0.9107321	0.2493056	-1.0585105	-2.0115443	-0.0698078	-0.7093641	-3.1873771	-0.6296110	0.4722171	-1.0280983	-0.5335278	-0.4631427	-0.7667049	-0.0188810	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	-0.7517573	-1.2024273	-0.7813405	0.9734290	1.0648922	0.1975911	0.0804964	-0.1035534	0.2970001	0.1627442	-0.3776906
2.5040049	0.4452930	1.8939007	-4.3825590	-1.1970300	0.7241760	3.1609066	0.2804503	-1.3357507	1.1498652	-0.2416110	-0.1655192	-1.7422677	1.2423341	0.2617237	-0.6945947	0.1759761	0.4057864	-0.7093641	-2.2521679	-1.5811049	0.4722171	-0.2815524	-0.5335278	-0.4631427	-1.1240181	0.2873801	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.2068218	-1.0157277	-1.2024273	-0.7813405	0.9734290	0.9767542	0.1839826	0.0613235	-0.0866315	1.0480802	0.6995387	-0.2048771
1.7635225	0.3022711	1.4747432	-4.3825590	0.3508672	3.5339007	2.5478689	-0.8775240	-1.0451284	-0.1403128	-0.2416110	-0.1655192	0.2548015	0.5129857	0.4739327	-0.5793101	-0.6267548	0.7363484	-0.7093641	-1.7343654	-0.4647902	0.4515612	-0.3728164	-0.5335278	-0.4631427	-1.1394242	0.4966298	-1.4290972	-0.7849217	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.7424211	-1.0542972	0.8894775	1.1148349	0.9734290	1.0801597	0.1647237	-0.0131299	-0.0583580	-0.0143037	-0.3588968	-0.6911786
1.5156237	-0.0129617	1.3754048	-4.3825590	0.1491911	3.4102418	2.3802827	0.1371349	-0.7239240	0.1028039	-0.2416110	2.8435806	-0.0833787	-0.1179987	0.5782899	-0.6121307	-0.2118106	0.6487932	-0.7093641	-1.6466687	-0.7011528	0.4722171	0.5707859	-0.5335278	2.0465777	-0.9326452	-0.2190505	-1.4290972	0.9300293	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.4319047	-0.5215700	0.9255706	1.2818974	0.8020628	1.1528553	0.1720294	-0.0345229	-0.0517680	0.2567754	0.0656445	-0.8134475
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1.0335598	-0.9447908	-1.8529628	-0.0862508	0.5940668	0.4728896	-0.2976194	0.5386858	0.9178725	-1.1028887	-0.2416110	11.5669416	0.3944659	-0.9107321	0.2789479	-0.2462546	0.9973484	-0.4988308	1.8568355	0.6675264	0.8341358	0.4722171	1.1128866	-0.5335278	2.2193379	0.9159201	-0.2051022	0.5869412	-0.7849217	-0.1128779	0.9627205	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	1.6558712	-1.2024273	-0.7813405	1.3163159	1.0113006	0.1919767	0.1105173	0.2157771	-1.1480371	-1.0638050	-0.0096942
0.9146868	-0.6036922	-1.8927126	-0.1432308	0.2242233	0.1789014	-0.6952914	0.7856713	0.5752263	-1.1028887	-0.2416110	-0.1655192	-0.1284720	-0.9107321	0.5552528	0.1025957	0.7873788	-0.1193563	1.5154156	0.4677229	0.1139497	0.4257124	0.4882681	1.9364074	-0.4631427	1.1197136	-0.3265755	0.6748461	-0.7849217	-0.1128779	1.0200015	4.0728408	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	1.1283514	1.1091757	-0.7813405	1.6079026	0.7837446	0.1877967	0.0973273	0.1817343	-1.2865973	-1.2155662	0.1192857
1.1052359	-0.2862466	-1.4975538	0.0671787	0.1768856	-1.8991883	0.0177658	0.2649183	-0.2276213	-0.2363715	-0.2416110	-0.1655192	-0.1065306	-0.7570370	-0.1310396	-1.4842718	1.2112895	-1.5361490	1.8688971	0.6600305	-0.0406418	0.4722171	1.0851941	-0.5335278	-0.4631427	0.6105541	-0.3098221	0.6597182	-0.7849217	-0.1128779	1.1779948	4.5028379	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.7894422	0.4962618	-1.2024273	-0.7813405	1.6592724	0.7410894	0.1904489	0.1416166	0.2258602	0.7292854	0.9786102	0.1868181
1.0446522	-0.0136502	-2.1505165	0.0785289	0.1302537	-0.5960238	0.2090842	0.4632836	0.1836177	-0.3230007	-0.2416110	-0.1655192	-0.2356120	0.0535965	0.1248362	-0.5745370	1.0883372	-1.5361490	1.9767846	0.6606270	0.5535163	0.4687688	-0.7303157	-0.5335278	-0.4631427	1.0128834	-0.0598623	0.6442183	-0.7849217	-0.1128779	1.0657407	-0.2161285	2.9413631	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	1.0627887	-1.2024273	1.2090360	0.8020628	1.2690767	0.1877168	0.1452051	0.2261440	-0.9392196	-0.8128572	0.2524100
1.0183739	-0.8043037	-1.3195287	-0.0440454	0.4745114	-1.3697861	-0.6304782	0.6415063	1.3252214	-1.1028887	-0.2416110	-0.1655192	0.4173160	-0.9107321	0.3361134	-1.1485087	1.1461364	-1.5361490	1.9118243	0.6735897	0.9943363	0.4722171	2.0572850	1.7771501	2.2373646	1.3113811	-0.0864659	0.4948966	-0.7849217	-0.1128779	1.0855736	4.5028379	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	1.5777284	-1.2024273	-0.7813405	1.2451515	1.0653986	0.1926225	0.1203266	0.2201068	-1.4964843	-1.2957401	-0.1260634
1.0445868	-0.1538384	-1.1030953	0.0758228	0.0633569	-1.4485418	-0.0967376	0.5157531	0.7456799	-1.1028887	-0.2416110	-0.1655192	-0.2043741	-0.9107321	0.0482348	-1.7247356	1.2228867	-1.5361490	-0.0975147	0.6646141	0.1365442	0.4722171	1.7679220	1.9388213	-0.4631427	1.1350133	-0.1874557	0.5549072	-0.7849217	-0.1128779	1.0657407	-0.2161285	2.9413631	6.2819793	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.8409862	0.9072276	-0.7813405	1.3163159	0.9466819	0.1918835	0.1473281	0.2240567	0.3625931	0.5082090	0.0033467
1.0193461	-0.4709592	-0.8071651	0.1161151	-0.0061888	-1.7696296	0.0263051	0.0890782	-0.4208332	0.6949008	-0.2416110	-0.1655192	-0.3221691	0.9698742	-0.4582505	-0.3862392	1.1759811	0.0812329	-0.7093641	0.6286913	0.3917231	-0.0596377	0.1453456	-0.5335278	-0.4631427	0.3937430	-0.1198934	0.7020283	-0.7849217	-0.1128779	1.1207102	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	0.4413023	-1.2024273	-0.7813405	0.9734290	1.1594996	0.1903044	0.1322515	0.2265789	0.4553071	0.6689750	-0.0324220
0.7704941	0.5328297	-0.6678449	-0.1313684	-1.2239327	0.1439709	-0.6248616	0.3780345	-0.1120158	1.3725874	-0.2416110	-0.1655192	-1.4780712	1.4751380	-0.0804973	-0.1064845	0.6186297	0.7680772	1.2580375	0.4821103	0.4711295	0.4357308	0.6736436	-0.5335278	-0.4631427	0.6701133	-0.0393987	0.6683254	-0.7849217	-0.1128779	1.1649661	4.9329899	2.9413631	6.2819793	-0.2945872	2.5035881	-0.0567962	-0.6042839	0.9665493	0.9406825	-0.7813405	0.8020628	1.2614452	0.1631283	0.0540698	0.1904805	-0.1756146	-0.0709090	-0.3076041
0.7698528	-0.0461416	-0.7452556	-0.3467252	-1.6296588	-0.3639810	-1.3432009	0.3279562	-0.2403203	1.3633885	-0.2416110	-0.1655192	-1.6116734	1.3251804	0.0726554	-0.1227481	0.6327097	0.5748005	1.2090269	0.3583425	0.1976421	0.2960964	0.3809274	-0.5335278	-0.4631427	0.7719061	-0.1983201	0.6830360	1.2739612	-0.1128779	1.2020110	-0.2161285	-0.3002999	-0.1390876	-0.2945872	3.3115666	-0.0567962	-0.9894272	0.9123570	-1.2024273	1.3650428	-0.9072150	-0.9131378	0.1608505	0.0759823	0.1693537	0.4511824	0.4831891	-0.2964140
0.9880977	-0.5850159	-1.2931888	-0.3829968	0.0104025	-0.4319388	-1.1199741	0.3878806	0.1017369	-0.3471058	-0.2416110	-0.1655192	-0.3740956	-0.3601765	0.5617630	-0.1339702	0.7610361	-0.0027857	1.5905974	0.4142253	0.4047341	0.4722171	-0.2254989	-0.5335278	-0.4631427	0.2206752	-0.1226806	0.6618281	-0.7849217	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	0.6591948	-1.2024273	1.2344786	-0.9072150	-0.9131378	0.1817268	0.1164738	0.1785964	-0.1431911	-0.1855945	-0.0725478
0.7369377	0.5642957	-0.4810215	-0.5984845	-1.2639808	-0.0118443	-1.0155203	-0.3244609	-1.1629855	1.2265724	-0.2416110	-0.1655192	-1.2239534	0.5184238	0.1460869	0.3867002	-0.1673132	0.7751630	0.1868859	0.3897232	-0.3489272	-8.7305008	0.6676447	-0.5335278	-0.4631427	0.1148188	0.5474337	-1.4290972	0.9300293	-0.1128779	0.8351781	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.4319047	-0.1101217	0.7989589	1.3144810	-0.9072150	-0.9131378	0.1168833	0.0525847	0.1570478	0.9694389	0.9491939	-0.3307362
0.0197808	0.5989323	-0.0039672	-0.5663583	-1.3665159	-0.1079565	0.5397642	-0.2877017	-0.6689654	1.1467954	-0.2416110	-0.1655192	-1.9606342	1.2318910	0.2440003	0.6967468	-0.4279688	0.7283702	-0.7093641	0.6091168	-0.6370987	-0.6227070	0.4863106	-0.5335278	-0.4631427	1.3026090	0.1623349	0.6013504	0.9300293	-0.1128779	0.9275866	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	-0.5578106	0.8298717	-0.7813405	-0.9072150	-0.9131378	0.0737230	0.1546532	0.1824022	0.3364133	0.0279424	-0.9513548
0.5103783	0.7611395	0.5723362	0.2959410	-0.6642086	-0.3994003	-0.4911821	0.3785485	-1.3482142	1.1455092	-0.2416110	-0.1655192	-0.9439898	0.9938712	0.1471852	0.4138851	0.6118605	0.5852279	0.5908708	0.2035972	-0.5023282	-0.9219664	0.3152728	1.8705656	-0.4631427	0.7024060	-0.0513391	0.6729922	1.2739612	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	3.3975921	2.7913150	-0.0567962	-0.7894422	-0.0430522	0.8433473	-0.7813405	1.2832837	0.9057248	0.1247044	0.0832092	0.1326641	0.8700931	0.7100586	-0.9001727
-0.0300048	0.7888970	0.2199620	-0.0776991	-0.4492820	-0.0701048	0.6576203	-0.5657865	-1.1626789	1.1986755	-0.2416110	-0.1655192	-0.6399085	0.1940620	0.2377659	0.5520123	-1.2167867	0.8547074	-0.7093641	0.5826615	-0.7090142	-0.2346037	-0.9787628	-0.5335278	-0.4631427	-0.3516118	0.1869775	0.7526934	0.9300293	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	2.5035881	-0.0567962	0.5250170	-1.1898459	0.6608507	-0.7813405	0.8020628	1.1521271	0.0767891	0.1894652	0.1741378	0.5716621	0.2809048	-1.0794044
2.7247421	1.3450365	1.9530508	-4.3825590	0.3446379	4.5902009	3.3387840	0.0586358	-0.4825502	1.1963227	-0.2416110	-0.1655192	0.1655223	1.5380296	-0.3631097	-1.7423764	-0.1357881	-1.5361490	-0.7093641	-3.2766023	0.0371378	-3.8219247	-0.2813196	-0.5335278	-0.4631427	-0.4327184	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	0.0270973	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1930034	0.0275292	-0.1527536	0.5692211	0.6038913	0.5984210
2.2533930	2.2976088	1.5224896	0.3010379	0.0577220	4.2280164	3.0282453	-0.5068261	-0.5468146	1.2107105	-0.2416110	-0.1655192	0.7233521	1.7719558	-0.1055768	-0.6429553	0.4670596	-1.5361490	-0.7093641	-0.7726840	-0.5901857	-0.2866240	1.9960486	-0.5335278	-0.4631427	-0.9626089	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	3.0611569	-0.3663205	-0.0567962	-0.6042839	-0.2732147	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1906945	-0.0366275	0.0490877	1.0199290	1.0146312	0.3046417
1.3808487	1.6865232	0.0780973	0.4387473	1.9492583	2.6835017	1.4963402	-3.1684987	1.4556399	-1.1028887	-0.2416110	-0.1655192	2.2391513	-0.9107321	-4.4973391	-8.3073542	-2.0115443	-1.5361490	-0.7093641	-3.4995135	-0.3132502	0.4722171	0.0904002	-0.5335278	-0.4631427	-0.7750846	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.0236306	-0.3822044	-1.2024273	-0.7813405	-0.9072150	-0.9131378	-7.7955680	-7.8028518	-7.7819186	1.0026278	1.2472649	1.1056816
1.3478521	1.2203379	-0.1042381	0.3341945	-0.0863422	1.2846306	0.3271836	-3.1684987	1.5119650	0.9766283	-0.2416110	-0.1655192	0.0749847	2.2647285	-4.4973391	-8.3073542	-2.0115443	-1.5361490	-0.7093641	-1.6281694	-0.6590308	0.4722171	2.5484432	-0.5335278	-0.4631427	-1.1043049	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	-0.3536354	0.8276787	-0.7813405	1.2000520	0.9371258	-7.7955680	-7.8028518	-7.7819186	0.5852573	0.6514599	1.1056816
1.0914929	0.0871439	-0.5689174	0.1838176	0.3335444	-1.8323062	-0.6001288	0.2614465	0.8201151	-1.1028887	-0.2416110	-0.1655192	0.0281460	-0.9107321	-0.2018539	0.0848185	1.2270370	-1.5361490	-0.7093641	0.7723230	1.0702304	0.4722171	0.7664629	1.7852585	2.2459047	0.1617271	-0.4902254	0.6684984	0.9300293	-0.1128779	1.0855736	-0.2161285	-0.3002999	-0.1390876	-0.2945872	2.5035881	-0.0567962	0.0236306	1.2338939	1.2047934	-0.7813405	0.8020628	1.3169406	0.1907839	0.1410480	0.2484096	-1.2267508	-0.9783760	0.0429058
0.9261104	0.2793468	-0.4059476	0.1059529	-1.2929589	-0.0328600	-0.6951686	0.2527627	0.2359393	1.2732282	-0.2416110	-0.1655192	-1.6754119	1.1223453	-0.1772631	0.2933324	0.7765312	0.8140821	-0.7093641	0.6656505	0.8145105	0.2315376	0.4776621	-0.5335278	-0.4631427	0.6800300	-0.2017209	0.5850207	-0.7849217	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	1.1378710	0.9421468	-0.7813405	0.9734290	1.1986628	0.1705929	0.0904033	0.2267059	-0.5816577	-0.3656763	-0.2526418
0.5919765	0.2960747	-0.3211731	-0.2141745	-2.6452932	0.6662508	0.2411965	0.0100518	-0.8719921	1.4015828	-0.2416110	-0.1655192	-2.4261980	1.7599350	-0.3577963	0.3536311	-0.0138127	0.9010619	-0.7093641	0.5535250	-0.3585267	0.0206010	0.1426633	-0.5335278	-0.4631427	-0.2961603	0.0731802	0.6870643	1.2025710	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	0.5764328	0.6731885	-0.7813405	1.1448570	0.9954130	0.1213328	0.0843522	0.1924850	-0.1019808	-0.1384383	-0.4520095
0.5769548	0.3207810	-0.1386452	-0.0855457	-1.8719420	-0.2470830	0.3420355	-0.0630626	-0.9718122	1.3003274	-0.2416110	-0.1655192	-1.6934080	1.6225645	-0.3177635	0.4862831	-2.0115443	0.8643687	-0.7093641	0.4591683	-0.9384104	0.1285391	0.1224043	-0.5335278	-0.4631427	-0.6888235	-0.1775967	-1.4290972	1.2025710	-0.1128779	0.6772291	-0.2161285	3.2663609	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.7211713	0.7781318	0.5297973	1.2599493	-0.9072150	-0.9131378	0.1329736	0.0973084	0.1832756	1.0826104	0.8522660	-0.3892172
0.9810375	-0.1997016	-0.2039209	0.1750888	-0.2711437	-0.8255880	-0.7314292	0.2281338	0.2371719	0.9597573	-0.2416110	3.7431920	-0.6597539	1.2635831	0.0939971	0.2035743	0.7875167	0.3763836	-0.7093641	0.6834407	0.9959477	0.2028977	0.2500967	-0.5335278	2.2375459	0.3340280	-0.0207358	0.7611563	0.9300293	-0.1128779	0.9931555	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	1.3498152	0.9931586	1.2891704	-0.9072150	-0.9131378	0.1738094	0.1198063	0.2345255	-0.5559219	-0.4754746	-0.2749981
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0.6238754	-2.5902245	-1.5665608	0.1282273	0.1034284	-0.8638655	-0.8700352	-3.1684987	2.2234056	-1.1028887	-0.2416110	-0.1655192	-0.2905013	-0.9107321	-4.4973391	-0.0859762	1.1231404	-1.5361490	-0.7093641	0.5912274	2.2771091	0.4722171	0.3343707	1.7521429	2.0000012	0.7970767	-0.4119425	0.4324275	-0.7849217	-0.1128779	0.9275866	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.5250170	2.2983618	-1.2024273	-0.7813405	1.0737029	1.2788134	0.1972650	0.1472603	0.1986399	-1.4907800	-1.4120593	0.2292144
0.6652263	-3.3067164	-1.6651976	0.1553409	-0.2175270	-0.3211708	-0.3556212	-3.1684987	2.2234056	-1.1028887	-0.2416110	-0.1655192	-0.6213664	-0.9107321	-4.4973391	-0.4355486	1.0782838	-1.5361490	-0.7093641	0.6819980	1.5475683	0.4722171	0.3058943	1.8362562	2.1847119	0.3898740	-0.1983275	0.4931326	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	1.1275793	1.0311373	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1954261	0.1538346	0.2141836	-0.7394315	-0.5786127	0.3036912
0.6355611	-1.0206880	-1.4893404	0.1802638	0.2557789	0.3645321	-0.1536721	-3.1684987	1.9806745	-1.1028887	-0.2416110	3.6465053	-0.0171365	-0.9107321	-4.4973391	-0.4170334	0.7922429	-1.5361490	-0.7093641	-0.0007711	0.1438521	0.4722171	2.7625164	1.6575899	1.7441541	0.0440211	-0.1887736	0.3610116	-0.7849217	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.1191818	0.2501188	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1919070	0.1283863	0.2056831	-3.1432069	-3.0893832	0.6439876
0.5479931	1.5996572	1.0546066	0.3126839	1.4268487	0.0491545	0.1148625	-1.5128687	-0.3055450	-1.1028887	5.6170694	1.9898242	1.6955342	-0.9107321	-2.1975791	-1.7921787	0.6648735	-1.5361490	-0.1482289	-1.2590657	0.5880687	0.4722171	0.2308868	1.8779640	1.9618372	1.0362803	-0.0682139	0.5213883	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	0.8733553	-1.2024273	-0.7813405	1.0737029	1.1223556	0.1834027	0.1540004	-0.0262824	-3.9841991	-3.8843240	-0.3112211
0.6958488	-3.7152365	-1.7272627	0.1615486	-0.1395004	-0.1759621	-0.2111284	-3.1684987	2.2234056	-1.1028887	-0.2416110	-0.1655192	-0.5094004	-0.9107321	-4.4973391	-0.3007111	0.9606534	-1.5361490	-0.7093641	0.7124836	1.0472000	0.4722171	1.5005225	1.8631988	2.1284073	0.2512365	0.1930706	0.5161044	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.7424211	0.7119164	-1.2024273	-0.7813405	1.1448570	1.1256271	0.1939543	0.1587459	0.2188705	-1.4861999	-1.2022213	0.4398175
0.7295890	-3.3075801	-1.7554381	0.1706703	0.0353180	-0.0915837	-0.0520288	-3.1684987	2.1891348	-1.1028887	-0.2416110	7.2081800	-0.3004423	-0.9107321	-4.4973391	-0.5564927	0.5444993	-1.5361490	-0.7093641	0.6470038	0.5083350	0.4722171	0.8991640	-0.5335278	2.0677709	0.2908276	-0.2484117	0.5550592	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.1191818	0.6758856	-1.2024273	-0.7813405	1.0737029	1.1149698	-7.7955680	-7.8028518	-7.7819186	0.9890100	1.2389155	1.1056816
0.7641795	-0.6224522	-2.1167121	0.1331322	-0.7743774	-1.4895254	-0.2577889	-1.3355179	1.9176356	-0.0790204	-0.2416110	-0.1655192	-1.3737277	1.0862459	-2.2358353	-0.6350417	1.0871605	-1.5361490	1.6982368	0.0295777	2.4495715	0.4722171	-0.8209490	2.0768430	-0.4631427	0.6912573	-0.4203333	0.6373022	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	1.2152581	2.0244149	-1.2024273	-0.7813405	1.1448570	1.2555304	0.1953284	0.1420107	0.2150929	-0.8234122	-0.5069308	0.2980362
0.7189708	-1.2553927	-1.9680439	0.1130268	-1.0980928	-1.9361672	-0.6481228	-1.2301612	2.0452170	0.7748357	-0.2416110	-0.1655192	-1.8370737	1.7238573	-2.1058477	-0.3056405	0.9900693	-1.5361490	1.7601503	0.5781693	2.5123629	0.4722171	-0.2012539	1.7467179	2.0634648	0.8765288	0.6177527	0.4326386	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.5250170	2.5731715	-1.2024273	-0.7813405	1.0737029	1.3006052	0.2007598	0.1372865	0.2061025	-1.5638648	-1.2876722	0.0912259
0.7242923	-1.2989464	-1.8694781	0.0481745	0.1178533	-1.1097980	-1.6020540	0.3913681	1.9100175	-1.1028887	2.3795348	-0.1655192	-0.2980879	-0.9107321	-0.1000316	0.1250748	1.0517878	-1.5361490	1.5828152	0.4925709	2.2800137	0.4722171	-0.1519738	1.7904106	2.1522253	0.6452677	-0.2701538	0.4755646	-0.7849217	-0.1128779	1.0855736	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.4319047	2.9608505	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1996343	0.1124953	0.1858714	-1.8634065	-1.6346765	0.2155543
0.9352516	-1.3793536	-3.0269529	0.0215361	0.0900540	0.1332152	-0.1066436	-0.1414825	2.0377199	-0.8662133	-0.2416110	-0.1655192	-0.3692318	-0.3089347	-0.6620418	0.0206950	0.7681656	-1.5361490	1.8300773	0.6846485	2.9304573	0.4722171	0.2054028	1.9100254	2.1582016	0.7810711	-0.1544723	0.4325190	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	0.2868788	3.2255853	-1.2024273	-0.7813405	1.2451515	1.2447437	0.1914616	0.1272668	0.2209386	-2.2095334	-2.0670853	0.1783289
0.8444331	-0.9330949	-2.9443530	0.0747295	-0.7695606	-0.9565209	-0.3344822	-0.6036707	1.8805892	0.1310209	-0.2416110	-0.1655192	-1.5238491	1.1997774	-1.3328933	-0.3090592	0.9778643	-1.5361490	1.8112041	0.0716776	2.5471763	0.4722171	-0.6926950	1.7248578	2.1822881	0.5215356	-0.4246885	0.5017085	-0.7849217	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.2706541	3.1618692	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1948107	0.1064054	0.2122564	-3.3992545	-3.2647966	0.3128996
-0.7153664	0.4502275	1.0481024	-0.0805202	-0.4000201	-0.9808023	-1.0769526	-0.2862954	0.2005249	0.8699766	-0.2416110	-0.1655192	-0.8646722	1.0463117	0.1751368	-0.0594924	-0.0348250	0.8218737	-0.7093641	-0.4416738	-0.2159140	0.4605887	-0.0186274	1.9011654	-0.4631427	-0.0177133	-0.4902254	0.7010200	-0.7849217	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	3.7341486	-0.3663205	-0.0567962	-2.0024503	1.1270342	0.9143624	-0.7813405	-0.9072150	-0.9131378	0.1573051	0.1341345	0.0544739	-1.3245569	-1.4023724	0.8187568
-0.5617197	-1.1270253	1.0423437	-0.0866456	0.1640141	-1.0020259	-0.4873752	-1.4301914	1.6399948	-1.1028887	-0.2416110	-0.1655192	-0.0591290	-0.9107321	0.1704439	-0.3722444	0.2216118	0.3719354	-0.7093641	-0.6805169	1.0168585	0.4722171	0.6459055	1.8146778	2.2398990	0.2306910	-0.3986840	0.5758925	1.2739612	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	3.3975921	-0.3663205	-0.0567962	-0.9894272	1.8693170	1.1994568	-0.7813405	-0.9072150	-0.9131378	0.1768587	0.1536592	0.0416061	-0.7557411	-0.6951816	0.8100547
-1.2082406	-1.2306736	1.0501724	-0.3414420	0.4114874	-0.0459608	-1.3977370	-0.4182376	1.4924198	-1.1028887	-0.2416110	-0.1655192	0.1295388	-0.9107321	0.2830407	-0.2881221	0.3509980	0.1653352	-0.7093641	-0.6501137	0.6138227	0.4689071	0.4828230	1.9898128	2.0124254	0.5441359	-0.2635801	0.5653819	1.2025710	-0.1128779	0.5193370	-0.2161285	-0.3002999	-0.1390876	3.3975921	-0.3663205	-0.0567962	-1.7081830	1.8935895	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1800239	0.1580294	0.0371551	-1.8954263	-1.7042597	0.8621822
-1.2218157	-2.1458777	1.0472711	-0.4187440	0.2164229	-0.0660772	-1.6659814	-0.7823979	1.7784410	-1.1028887	-0.2416110	-0.1655192	-0.1385491	-0.9107321	0.1004149	-0.0712315	-1.8559490	-0.2305276	-0.7093641	-0.6511766	0.8861615	0.4612104	1.4189413	1.8007144	2.1102863	0.2596872	-0.2988330	0.5505589	1.1019643	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	4.0707657	-0.3663205	-0.0567962	-0.6042839	1.4513650	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1820769	0.1416890	0.0360817	-0.8128519	-0.5952688	1.0928640
-1.3708028	-0.8472663	-0.1926501	0.4392459	-0.8000716	0.1732351	1.0232963	-0.0980002	1.6102044	-0.3050653	-0.2416110	-0.1655192	-1.6511890	1.3478997	0.0241304	0.5400138	0.8896999	-0.4496998	-0.7093641	0.4328218	-0.9187399	0.4722171	0.8732309	1.6078827	2.0220934	0.4204362	-0.4902254	0.6322432	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.0024503	0.3060351	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1890920	0.1598796	0.2162693	-2.1040048	-1.7680941	-0.1275653
-0.8522738	0.7628507	-0.3887801	0.4533951	-1.1483852	0.3979112	0.8408895	-0.6615732	0.0462667	0.7735091	-0.2416110	-0.1655192	-0.6348772	-0.9107321	-0.1275297	0.6154390	-0.4640421	1.0087909	-0.7093641	0.8664643	-1.9146573	0.0456755	1.4897880	-0.5335278	-0.4631427	-1.3498798	0.0545749	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.0024503	-0.8573343	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1326908	0.2640898	0.2559705	0.5623707	0.9042770	-0.0329944
-0.8941916	-1.6612829	-0.2745011	0.4293331	-0.4606625	-1.0769090	1.0552532	-0.0225813	2.0591483	-1.1028887	-0.2416110	-0.1655192	-1.0144047	-0.9107321	-0.4205530	-0.0047809	0.8834583	-1.5361490	-0.7093641	0.6382788	0.1164273	0.4675777	1.8028429	1.7637571	2.1385769	-0.2615317	-0.3268318	0.4430654	-0.7849217	-0.1128779	0.6772291	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.8174868	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1886108	0.1743173	0.2339778	-1.8691041	-1.4944695	0.3226523
-0.9025533	-1.6225502	-0.2231239	0.4240828	-1.2092209	-0.3017642	1.0880789	-3.1684987	1.8622718	-0.1751019	-0.2416110	-0.1655192	-2.1667970	1.1801078	-2.0466775	0.5469642	0.9632107	-1.5361490	-0.7093641	0.3444656	0.4767794	0.4722171	-2.0289867	1.8660741	2.1791259	0.2694600	-0.3603655	0.5104978	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	0.9731492	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1906266	0.1383557	0.2280761	-2.1652121	-1.5199192	-0.3522967
-0.7212197	0.9578551	-0.5150556	0.4420828	-1.5211638	0.5167801	0.9272074	-1.6359655	0.4942077	1.3319873	-0.2416110	-0.1655192	-1.4518673	1.0570459	0.0761848	0.4923641	-0.8001192	1.0620990	-0.7093641	0.9936102	-1.5500890	0.3569701	-0.3117378	-0.5335278	-0.4631427	-0.6985375	-0.4902254	-1.4290972	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-2.0024503	-0.4314683	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.0936797	0.3186799	0.2600218	-0.9413963	-0.5217222	0.4892643
-0.6126005	-0.7077031	-0.3145347	0.4183489	-1.7711304	-1.6476595	0.9927371	-3.1684987	1.6964022	0.6937097	-0.2416110	-0.1655192	-2.1648864	1.6494836	-0.2975385	0.4606745	0.4802486	0.6670032	1.4422589	0.5358234	-0.3314381	0.4659292	1.1190239	1.6706287	2.0881802	0.1266613	-0.4902254	0.5313346	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.9894272	0.2943173	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1821135	0.2227467	0.2307131	-1.4768446	-1.0125985	-0.3674272
-0.3242173	0.3496063	-0.3357717	0.4010168	-1.5381402	-0.7297678	0.8567485	-0.0082585	1.3178164	0.9872085	-0.2416110	-0.1655192	-1.3303268	0.3103970	-0.1873932	0.2963027	0.6375892	0.7910801	-0.7093641	0.6048476	0.1150764	0.4722171	2.3415351	1.8274305	2.0235190	0.7159974	-0.4902254	0.6013136	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	1.1296676	-1.2024273	-0.7813405	-0.9072150	-0.9131378	0.1720495	0.2868188	0.2388820	-1.3491480	-1.0770065	-0.3061399
-0.1229755	-0.3740460	-0.3020525	0.3782214	-0.1970433	-1.3713362	0.7333711	0.4828768	0.8006936	-1.0153661	-0.2416110	-0.1655192	-0.6990035	0.9082337	0.3400542	0.4715302	0.8454156	0.3592098	-0.7093641	0.6201360	-0.7636133	0.4300341	-0.9435994	-0.5335278	-0.4631427	-0.3885831	-0.2086361	-1.4290972	0.9300293	-0.1128779	0.7696186	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-0.6042839	-0.4758021	0.9193252	-0.7813405	-0.9072150	-0.9131378	0.1863388	0.1838340	0.2328716	0.4775876	0.8545113	0.1287156
-0.6691769	0.8445447	-0.6034381	0.4194282	-2.1503066	0.6212286	0.7294676	-1.3134608	-0.2242970	1.4478214	-0.2416110	-0.1655192	-1.8675572	1.2242620	-0.1119268	0.3683664	-0.9556598	1.0824987	-0.7093641	1.0408001	-1.3410404	-0.2346174	0.6280498	-0.5335278	-0.4631427	-0.7795828	-0.4902254	0.5324644	-0.7849217	-0.1128779	-1.0555442	-0.2161285	-0.3002999	-0.1390876	-0.2945872	-0.3663205	-0.0567962	-1.4449486	-0.5712797	0.8018620	-0.7813405	-0.9072150	-0.9131378	0.0783115	0.2950352	0.2621456	-0.3150179	0.0208781	0.6754504

No missing data is found. Handle missing values if any, possibly through imputation

3.3 Identify multi-collinear variables

Compute the correlation matrix and identify highly correlated variables:

Code

#df_pre_pca_abb <- df_pre_pca
# Abbreviate column names using R's built-in abbreviate function
#abbrev_colnames <- abbreviate(colnames(df_pre_pca_abb))

# Assign the abbreviated names back to the dataframe
#colnames(df_pre_pca_abb) <- abbrev_colnames

# Recalculate and plot the correlation matrix
cor_matrix <- cor(df_pre_pca) |> round(digits = 2)

# Convert the matrix to a data frame
cor_matrix_df <- as.data.frame(cor_matrix)

# Add row names as a new column
cor_matrix_df$Predictors <- rownames(cor_matrix)

# Move the 'RowNames' column to the first position
cor_matrix_df <- cor_matrix_df|> select(Predictors, everything())



# Create the gt table
cor_matrix_df|>
  gt()|>
  data_color(
    columns = -Predictors,  # Exclude the 'RowNames' column from colorization
    colors = scales::col_numeric(
      palette = c("darkred", "white", "darkblue"),
      domain = c(-1, 1)
    )
  ) |> tab_options(container.overflow.x = TRUE, container.overflow.y = TRUE)

Predictors	distance_to_plantation	distance_to_road	distance_to_commodity_processing_factory	distance_to_plantation_concession	distance_to_forest	distance_to_river	distance_to_burned_area	percentage_of_agricultural_area_small_holder_in_the_village	percentage_of_plantation_area_per_sub_district	percentage_of_forested_area_in_the_sub_district	percentage_of_shrubland_in_the_sub_district	percentage_of_water_area_compared_to_sub_district_area	distance_to_deforestation	percentage_deforestation_area_size	arable_land_percent	erosion_risk_t_ha_1_yr_1	indeks_bahaya_banjir	indeks_bahaya_longsor	buffer_to_500m_irigated_land	aridity_index	total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	rasio_elektrifikasi	rasio_sekolah_tinggi_sma_sederajat	rasio_pt	rasio_rs	rasio_faskes_1	rasio_pasar	rasio_minimarket_swalayan	banyak_kejadian_tanah_longsor_2018_2019	korban_jiwa_tanah_longsor_2018_2019	banyak_kejadian_banjir_2018_2019	korban_jiwa_banjir_2018_2019	banyak_kejadian_banjir_bandang_2018_2019	korban_jiwa_banjir_bandang_2018_2019	banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	banyak_kejadian_kekeringan_lahan_2018_2019	korban_jiwa_kekeringan_lahan_2018_2019	jumlah_sistem_peringatan_dini_bencana_alam	persentase_sistem_peringatan_dini_bencana_alam	rasio_embung_di_kecamatan	rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	annual_mean_temp	temp_change	annual_mean_prec	rasio_40pers_ekon_rendah_rt	rasio_40pers_ekon_rendah_indv	prec_change
distance_to_plantation	1.00	0.05	0.16	-0.42	-0.01	0.32	0.03	-0.21	-0.04	0.01	0.08	0.08	0.04	0.03	-0.18	-0.26	-0.13	-0.11	-0.16	-0.30	0.00	-0.04	0.07	0.03	0.01	-0.06	0.15	-0.19	-0.07	0.07	-0.03	0.03	0.10	0.13	-0.07	-0.03	-0.02	-0.11	0.07	0.09	-0.11	0.10	0.09	-0.11	-0.13	-0.14	0.13	0.09	0.07
distance_to_road	0.05	1.00	0.21	-0.01	-0.48	0.29	0.17	-0.10	-0.58	0.68	0.07	-0.13	-0.33	0.56	0.09	-0.05	-0.41	0.49	-0.20	0.09	-0.45	-0.29	-0.10	-0.34	-0.37	-0.22	0.16	-0.32	0.25	0.02	-0.03	-0.04	-0.06	-0.03	0.07	0.09	0.00	-0.05	-0.50	0.08	0.09	0.03	0.01	-0.05	0.00	0.00	0.32	0.28	0.13
distance_to_commodity_processing_factory	0.16	0.21	1.00	-0.30	0.15	0.37	0.23	0.11	-0.21	0.03	0.16	-0.16	0.19	0.03	0.28	-0.23	-0.01	-0.06	-0.17	-0.63	0.00	-0.03	-0.12	-0.16	-0.17	-0.06	0.15	0.00	-0.10	-0.01	0.08	-0.01	-0.03	-0.01	0.12	0.09	-0.09	0.14	-0.09	0.33	0.21	0.00	0.01	0.05	0.01	-0.05	0.06	-0.06	-0.46
distance_to_plantation_concession	-0.42	-0.01	-0.30	1.00	-0.06	-0.55	-0.46	0.15	0.04	0.03	0.07	-0.01	-0.04	-0.01	-0.08	0.21	0.02	0.05	0.06	0.62	0.02	-0.05	0.01	0.06	0.02	0.06	-0.26	0.11	0.07	-0.04	0.02	-0.03	-0.13	-0.15	0.04	0.01	0.03	0.09	-0.04	0.03	0.00	0.03	0.02	-0.06	0.00	0.02	-0.06	0.01	0.08
distance_to_forest	-0.01	-0.48	0.15	-0.06	1.00	-0.05	-0.05	0.37	0.30	-0.79	0.19	0.05	0.89	-0.72	0.25	-0.24	0.31	-0.51	0.20	-0.45	0.34	0.29	-0.09	0.04	0.02	0.23	-0.06	0.21	-0.31	-0.07	0.03	0.04	0.02	-0.05	-0.03	-0.03	-0.02	0.25	0.23	0.00	0.07	-0.01	0.02	-0.04	-0.09	-0.13	-0.11	-0.15	-0.19
distance_to_river	0.32	0.29	0.37	-0.55	-0.05	1.00	0.41	-0.25	-0.24	0.16	0.00	0.02	0.01	0.14	-0.06	-0.24	-0.40	0.15	-0.33	-0.36	-0.22	-0.11	-0.04	-0.27	-0.22	-0.21	0.18	-0.30	0.05	0.05	-0.24	-0.13	-0.11	-0.07	0.05	-0.02	0.01	-0.11	-0.18	0.07	0.04	-0.03	-0.02	-0.17	-0.19	-0.20	0.17	0.10	-0.11
distance_to_burned_area	0.03	0.17	0.23	-0.46	-0.05	0.41	1.00	-0.20	-0.01	0.09	-0.04	-0.02	-0.10	0.21	-0.02	-0.11	-0.04	0.00	-0.17	-0.27	-0.17	-0.03	0.01	-0.10	-0.03	-0.14	0.20	-0.15	-0.04	-0.11	-0.11	-0.11	-0.16	-0.04	-0.02	-0.03	0.01	-0.01	-0.20	-0.19	0.12	0.03	0.02	-0.08	-0.10	-0.10	-0.01	-0.03	-0.20
percentage_of_agricultural_area_small_holder_in_the_village	-0.21	-0.10	0.11	0.15	0.37	-0.25	-0.20	1.00	-0.15	-0.22	0.07	-0.09	0.36	-0.26	0.78	0.23	0.28	-0.05	0.25	-0.04	0.14	0.11	-0.16	-0.09	-0.15	0.12	-0.13	0.21	-0.01	-0.01	0.22	0.12	0.12	0.05	-0.04	0.09	0.03	0.15	0.06	0.22	0.19	-0.04	-0.02	0.39	0.38	0.36	0.05	0.01	-0.20
percentage_of_plantation_area_per_sub_district	-0.04	-0.58	-0.21	0.04	0.30	-0.24	-0.01	-0.15	1.00	-0.40	0.04	0.09	0.20	-0.25	-0.30	-0.20	0.47	-0.57	0.35	-0.16	0.59	0.28	0.16	0.48	0.47	0.29	-0.18	0.38	-0.34	-0.02	0.10	-0.02	0.04	0.03	0.00	-0.03	0.04	0.05	0.66	-0.32	-0.13	0.02	0.02	-0.14	-0.18	-0.19	-0.51	-0.47	0.04
percentage_of_forested_area_in_the_sub_district	0.01	0.68	0.03	0.03	-0.79	0.16	0.09	-0.22	-0.40	1.00	-0.10	-0.09	-0.74	0.81	-0.07	0.17	-0.34	0.56	-0.17	0.33	-0.30	-0.34	-0.02	-0.21	-0.22	-0.24	0.13	-0.19	0.30	0.10	0.00	-0.05	-0.01	0.02	0.12	0.14	0.04	-0.07	-0.30	0.09	0.04	0.06	0.05	0.03	0.06	0.10	0.28	0.26	0.08
percentage_of_shrubland_in_the_sub_district	0.08	0.07	0.16	0.07	0.19	0.00	-0.04	0.07	0.04	-0.10	1.00	0.01	0.21	-0.03	0.01	-0.13	0.17	-0.23	0.05	-0.15	0.12	0.02	-0.08	0.01	0.03	0.04	-0.01	0.11	-0.16	-0.03	0.18	-0.05	-0.07	-0.03	0.04	0.02	-0.01	0.12	0.06	0.05	0.13	0.01	0.02	0.04	0.03	0.01	-0.19	-0.20	-0.08
percentage_of_water_area_compared_to_sub_district_area	0.08	-0.13	-0.16	-0.01	0.05	0.02	-0.02	-0.09	0.09	-0.09	0.01	1.00	0.01	-0.06	-0.17	-0.02	0.07	-0.06	0.04	0.07	0.08	0.06	0.13	0.01	0.23	0.07	-0.02	0.03	-0.07	-0.02	0.02	-0.04	-0.05	-0.02	-0.01	-0.03	-0.01	-0.04	0.12	-0.07	-0.06	0.06	0.05	-0.19	-0.19	-0.18	-0.12	-0.09	0.07
distance_to_deforestation	0.04	-0.33	0.19	-0.04	0.89	0.01	-0.10	0.36	0.20	-0.74	0.21	0.01	1.00	-0.79	0.22	-0.27	0.21	-0.42	0.14	-0.46	0.22	0.24	-0.12	-0.03	-0.05	0.19	-0.09	0.10	-0.27	-0.10	0.02	0.02	0.04	-0.07	-0.03	-0.04	0.02	0.20	0.12	0.02	0.06	-0.07	-0.05	-0.06	-0.10	-0.15	-0.03	-0.07	-0.06
percentage_deforestation_area_size	0.03	0.56	0.03	-0.01	-0.72	0.14	0.21	-0.26	-0.25	0.81	-0.03	-0.06	-0.79	1.00	-0.13	0.09	-0.23	0.34	-0.09	0.26	-0.21	-0.26	0.04	-0.12	-0.11	-0.20	0.13	-0.15	0.21	0.09	0.04	-0.01	-0.06	0.03	0.14	0.09	-0.05	-0.06	-0.21	0.01	0.06	0.10	0.08	-0.01	0.01	0.04	0.12	0.13	0.04
arable_land_percent	-0.18	0.09	0.28	-0.08	0.25	-0.06	-0.02	0.78	-0.30	-0.07	0.01	-0.17	0.22	-0.13	1.00	0.37	0.06	0.20	0.10	-0.09	-0.04	0.05	-0.17	-0.22	-0.26	0.06	0.03	0.07	0.07	0.03	0.12	0.07	0.10	0.03	0.04	0.04	0.01	0.06	-0.09	0.25	0.23	-0.08	-0.08	0.54	0.53	0.51	0.17	0.11	-0.27
erosion_risk_t_ha_1_yr_1	-0.26	-0.05	-0.23	0.21	-0.24	-0.24	-0.11	0.23	-0.20	0.17	-0.13	-0.02	-0.27	0.09	0.37	1.00	-0.12	0.46	-0.10	0.54	-0.15	-0.14	-0.05	-0.07	-0.04	-0.06	-0.04	0.00	0.31	0.05	-0.06	-0.09	0.03	-0.04	0.05	0.05	0.02	-0.03	-0.16	0.10	0.06	-0.05	-0.06	0.57	0.60	0.63	0.09	0.12	0.08
indeks_bahaya_banjir	-0.13	-0.41	-0.01	0.02	0.31	-0.40	-0.04	0.28	0.47	-0.34	0.17	0.07	0.21	-0.23	0.06	-0.12	1.00	-0.63	0.56	-0.23	0.55	0.30	0.00	0.32	0.27	0.33	-0.07	0.56	-0.41	-0.11	0.49	0.18	0.06	0.04	-0.06	0.04	-0.06	0.21	0.50	-0.15	0.07	0.11	0.13	0.23	0.16	0.14	-0.44	-0.44	-0.22
indeks_bahaya_longsor	-0.11	0.49	-0.06	0.05	-0.51	0.15	0.00	-0.05	-0.57	0.56	-0.23	-0.06	-0.42	0.34	0.20	0.46	-0.63	1.00	-0.48	0.43	-0.49	-0.25	0.00	-0.34	-0.30	-0.22	0.08	-0.31	0.50	0.10	-0.17	-0.13	-0.04	-0.03	0.06	0.06	0.05	-0.15	-0.47	0.27	0.00	-0.06	-0.07	0.12	0.18	0.22	0.37	0.37	0.13
buffer_to_500m_irigated_land	-0.16	-0.20	-0.17	0.06	0.20	-0.33	-0.17	0.25	0.35	-0.17	0.05	0.04	0.14	-0.09	0.10	-0.10	0.56	-0.48	1.00	-0.08	0.37	0.18	-0.07	0.18	0.12	0.21	-0.08	0.31	-0.32	-0.06	0.22	0.09	0.16	0.00	-0.01	0.10	-0.04	0.11	0.36	-0.23	0.12	0.09	0.08	0.12	0.09	0.07	-0.24	-0.22	0.07
aridity_index	-0.30	0.09	-0.63	0.62	-0.45	-0.36	-0.27	-0.04	-0.16	0.33	-0.15	0.07	-0.46	0.26	-0.09	0.54	-0.23	0.43	-0.08	1.00	-0.22	-0.17	0.07	-0.02	0.02	-0.07	-0.13	-0.10	0.32	0.05	-0.08	-0.04	-0.15	-0.12	0.01	-0.04	0.06	-0.08	-0.21	-0.07	-0.06	0.08	0.06	0.11	0.19	0.27	0.06	0.15	0.27
total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	0.00	-0.45	0.00	0.02	0.34	-0.22	-0.17	0.14	0.59	-0.30	0.12	0.08	0.22	-0.21	-0.04	-0.15	0.55	-0.49	0.37	-0.22	1.00	0.26	0.02	0.44	0.44	0.41	-0.12	0.58	-0.23	0.00	0.30	0.09	0.12	0.07	0.08	0.04	-0.12	0.52	0.81	0.02	0.07	0.13	0.16	0.11	0.05	0.04	-0.50	-0.53	-0.32
rasio_elektrifikasi	-0.04	-0.29	-0.03	-0.05	0.29	-0.11	-0.03	0.11	0.28	-0.34	0.02	0.06	0.24	-0.26	0.05	-0.14	0.30	-0.25	0.18	-0.17	0.26	1.00	0.14	0.20	0.19	0.22	-0.02	0.30	-0.16	0.02	0.05	0.05	0.11	0.06	0.06	0.01	0.03	0.00	0.30	-0.09	-0.05	0.01	0.03	0.00	-0.04	-0.05	-0.32	-0.32	-0.05
rasio_sekolah_tinggi_sma_sederajat	0.07	-0.10	-0.12	0.01	-0.09	-0.04	0.01	-0.16	0.16	-0.02	-0.08	0.13	-0.12	0.04	-0.17	-0.05	0.00	0.00	-0.07	0.07	0.02	0.14	1.00	0.29	0.31	0.00	-0.05	0.06	0.06	0.12	0.04	0.01	0.03	0.14	0.09	-0.05	-0.12	-0.07	0.07	0.02	-0.13	-0.01	-0.01	-0.10	-0.10	-0.08	-0.20	-0.17	0.00
rasio_pt	0.03	-0.34	-0.16	0.06	0.04	-0.27	-0.10	-0.09	0.48	-0.21	0.01	0.01	-0.03	-0.12	-0.22	-0.07	0.32	-0.34	0.18	-0.02	0.44	0.20	0.29	1.00	0.65	0.23	-0.10	0.33	-0.11	0.00	0.10	0.03	-0.02	0.05	0.08	0.03	-0.03	0.05	0.48	-0.16	-0.13	0.03	0.05	0.08	0.06	0.07	-0.58	-0.53	-0.02
rasio_rs	0.01	-0.37	-0.17	0.02	0.02	-0.22	-0.03	-0.15	0.47	-0.22	0.03	0.23	-0.05	-0.11	-0.26	-0.04	0.27	-0.30	0.12	0.02	0.44	0.19	0.31	0.65	1.00	0.19	-0.10	0.25	-0.10	-0.05	0.05	-0.06	-0.01	0.01	0.05	0.00	-0.03	0.05	0.48	-0.21	-0.18	-0.05	-0.03	0.00	-0.02	-0.01	-0.63	-0.58	0.03
rasio_faskes_1	-0.06	-0.22	-0.06	0.06	0.23	-0.21	-0.14	0.12	0.29	-0.24	0.04	0.07	0.19	-0.20	0.06	-0.06	0.33	-0.22	0.21	-0.07	0.41	0.22	0.00	0.23	0.19	1.00	-0.09	0.25	-0.17	-0.05	0.19	0.12	0.06	0.06	0.01	0.06	-0.02	0.14	0.39	-0.01	0.01	0.09	0.10	0.09	0.07	0.06	-0.26	-0.27	-0.12
rasio_pasar	0.15	0.16	0.15	-0.26	-0.06	0.18	0.20	-0.13	-0.18	0.13	-0.01	-0.02	-0.09	0.13	0.03	-0.04	-0.07	0.08	-0.08	-0.13	-0.12	-0.02	-0.05	-0.10	-0.10	-0.09	1.00	-0.14	0.01	0.00	-0.07	-0.01	-0.03	-0.02	-0.03	-0.02	-0.03	0.02	-0.15	-0.03	0.13	-0.03	-0.04	0.05	0.04	0.04	0.06	0.00	-0.05
rasio_minimarket_swalayan	-0.19	-0.32	0.00	0.11	0.21	-0.30	-0.15	0.21	0.38	-0.19	0.11	0.03	0.10	-0.15	0.07	0.00	0.56	-0.31	0.31	-0.10	0.58	0.30	0.06	0.33	0.25	0.25	-0.14	1.00	-0.16	-0.11	0.37	0.12	0.07	0.05	0.08	0.02	-0.08	0.33	0.45	0.03	0.07	0.16	0.18	0.15	0.11	0.10	-0.41	-0.42	-0.21
banyak_kejadian_tanah_longsor_2018_2019	-0.07	0.25	-0.10	0.07	-0.31	0.05	-0.04	-0.01	-0.34	0.30	-0.16	-0.07	-0.27	0.21	0.07	0.31	-0.41	0.50	-0.32	0.32	-0.23	-0.16	0.06	-0.11	-0.10	-0.17	0.01	-0.16	1.00	0.17	-0.05	-0.12	0.02	0.02	0.21	0.15	0.06	-0.02	-0.25	0.17	0.03	0.00	-0.01	0.04	0.09	0.12	0.22	0.21	0.13
korban_jiwa_tanah_longsor_2018_2019	0.07	0.02	-0.01	-0.04	-0.07	0.05	-0.11	-0.01	-0.02	0.10	-0.03	-0.02	-0.10	0.09	0.03	0.05	-0.11	0.10	-0.06	0.05	0.00	0.02	0.12	0.00	-0.05	-0.05	0.00	-0.11	0.17	1.00	-0.02	-0.02	0.19	0.20	0.06	-0.04	-0.01	-0.09	0.06	0.07	0.03	-0.02	-0.05	0.01	0.00	0.01	0.06	0.03	-0.04
banyak_kejadian_banjir_2018_2019	-0.03	-0.03	0.08	0.02	0.03	-0.24	-0.11	0.22	0.10	0.00	0.18	0.02	0.02	0.04	0.12	-0.06	0.49	-0.17	0.22	-0.08	0.30	0.05	0.04	0.10	0.05	0.19	-0.07	0.37	-0.05	-0.02	1.00	0.23	0.09	0.04	0.03	0.15	-0.06	0.18	0.23	0.14	0.18	0.17	0.17	0.15	0.12	0.11	-0.14	-0.17	-0.19
korban_jiwa_banjir_2018_2019	0.03	-0.04	-0.01	-0.03	0.04	-0.13	-0.11	0.12	-0.02	-0.05	-0.05	-0.04	0.02	-0.01	0.07	-0.09	0.18	-0.13	0.09	-0.04	0.09	0.05	0.01	0.03	-0.06	0.12	-0.01	0.12	-0.12	-0.02	0.23	1.00	0.14	0.17	-0.02	0.02	-0.01	0.05	0.07	0.05	-0.04	0.15	0.13	0.04	0.02	0.02	0.02	0.01	-0.12
banyak_kejadian_banjir_bandang_2018_2019	0.10	-0.06	-0.03	-0.13	0.02	-0.11	-0.16	0.12	0.04	-0.01	-0.07	-0.05	0.04	-0.06	0.10	0.03	0.06	-0.04	0.16	-0.15	0.12	0.11	0.03	-0.02	-0.01	0.06	-0.03	0.07	0.02	0.19	0.09	0.14	1.00	0.46	0.04	0.08	-0.02	-0.04	0.17	0.12	0.06	0.01	0.03	0.05	0.02	0.02	0.07	0.04	0.09
korban_jiwa_banjir_bandang_2018_2019	0.13	-0.03	-0.01	-0.15	-0.05	-0.07	-0.04	0.05	0.03	0.02	-0.03	-0.02	-0.07	0.03	0.03	-0.04	0.04	-0.03	0.00	-0.12	0.07	0.06	0.14	0.05	0.01	0.06	-0.02	0.05	0.02	0.20	0.04	0.17	0.46	1.00	-0.04	0.10	-0.01	-0.06	0.13	0.12	-0.02	0.01	-0.01	0.02	0.01	0.00	0.04	0.03	0.01
banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	-0.07	0.07	0.12	0.04	-0.03	0.05	-0.02	-0.04	0.00	0.12	0.04	-0.01	-0.03	0.14	0.04	0.05	-0.06	0.06	-0.01	0.01	0.08	0.06	0.09	0.08	0.05	0.01	-0.03	0.08	0.21	0.06	0.03	-0.02	0.04	-0.04	1.00	0.16	-0.02	0.01	0.09	0.03	0.08	0.00	-0.02	0.03	0.03	0.03	-0.07	-0.07	0.02
banyak_kejadian_kekeringan_lahan_2018_2019	-0.03	0.09	0.09	0.01	-0.03	-0.02	-0.03	0.09	-0.03	0.14	0.02	-0.03	-0.04	0.09	0.04	0.05	0.04	0.06	0.10	-0.04	0.04	0.01	-0.05	0.03	0.00	0.06	-0.02	0.02	0.15	-0.04	0.15	0.02	0.08	0.10	0.16	1.00	0.18	0.03	0.03	0.15	0.02	0.04	0.05	0.04	0.04	0.03	0.03	0.01	0.01
korban_jiwa_kekeringan_lahan_2018_2019	-0.02	0.00	-0.09	0.03	-0.02	0.01	0.01	0.03	0.04	0.04	-0.01	-0.01	0.02	-0.05	0.01	0.02	-0.06	0.05	-0.04	0.06	-0.12	0.03	-0.12	-0.03	-0.03	-0.02	-0.03	-0.08	0.06	-0.01	-0.06	-0.01	-0.02	-0.01	-0.02	0.18	1.00	-0.12	-0.06	-0.07	-0.04	-0.05	-0.05	0.00	0.02	0.01	0.02	0.03	0.10
jumlah_sistem_peringatan_dini_bencana_alam	-0.11	-0.05	0.14	0.09	0.25	-0.11	-0.01	0.15	0.05	-0.07	0.12	-0.04	0.20	-0.06	0.06	-0.03	0.21	-0.15	0.11	-0.08	0.52	0.00	-0.07	0.05	0.05	0.14	0.02	0.33	-0.02	-0.09	0.18	0.05	-0.04	-0.06	0.01	0.03	-0.12	1.00	-0.07	0.21	0.24	0.16	0.19	0.10	0.08	0.06	0.03	-0.01	-0.30
persentase_sistem_peringatan_dini_bencana_alam	0.07	-0.50	-0.09	-0.04	0.23	-0.18	-0.20	0.06	0.66	-0.30	0.06	0.12	0.12	-0.21	-0.09	-0.16	0.50	-0.47	0.36	-0.21	0.81	0.30	0.07	0.48	0.48	0.39	-0.15	0.45	-0.25	0.06	0.23	0.07	0.17	0.13	0.09	0.03	-0.06	-0.07	1.00	-0.12	-0.09	0.04	0.06	0.07	0.01	0.00	-0.60	-0.61	-0.17
rasio_embung_di_kecamatan	0.09	0.08	0.33	0.03	0.00	0.07	-0.19	0.22	-0.32	0.09	0.05	-0.07	0.02	0.01	0.25	0.10	-0.15	0.27	-0.23	-0.07	0.02	-0.09	0.02	-0.16	-0.21	-0.01	-0.03	0.03	0.17	0.07	0.14	0.05	0.12	0.12	0.03	0.15	-0.07	0.21	-0.12	1.00	0.16	0.08	0.09	0.08	0.07	0.06	0.25	0.18	-0.31
rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	-0.11	0.09	0.21	0.00	0.07	0.04	0.12	0.19	-0.13	0.04	0.13	-0.06	0.06	0.06	0.23	0.06	0.07	0.00	0.12	-0.06	0.07	-0.05	-0.13	-0.13	-0.18	0.01	0.13	0.07	0.03	0.03	0.18	-0.04	0.06	-0.02	0.08	0.02	-0.04	0.24	-0.09	0.16	1.00	0.05	0.05	0.10	0.08	0.08	0.08	0.01	-0.27
jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	0.10	0.03	0.00	0.03	-0.01	-0.03	0.03	-0.04	0.02	0.06	0.01	0.06	-0.07	0.10	-0.08	-0.05	0.11	-0.06	0.09	0.08	0.13	0.01	-0.01	0.03	-0.05	0.09	-0.03	0.16	0.00	-0.02	0.17	0.15	0.01	0.01	0.00	0.04	-0.05	0.16	0.04	0.08	0.05	1.00	0.97	-0.07	-0.08	-0.07	0.02	0.00	-0.11
rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	0.09	0.01	0.01	0.02	0.02	-0.02	0.02	-0.02	0.02	0.05	0.02	0.05	-0.05	0.08	-0.08	-0.06	0.13	-0.07	0.08	0.06	0.16	0.03	-0.01	0.05	-0.03	0.10	-0.04	0.18	-0.01	-0.05	0.17	0.13	0.03	-0.01	-0.02	0.05	-0.05	0.19	0.06	0.09	0.05	0.97	1.00	-0.05	-0.06	-0.05	0.00	-0.02	-0.14
annual_mean_temp	-0.11	-0.05	0.05	-0.06	-0.04	-0.17	-0.08	0.39	-0.14	0.03	0.04	-0.19	-0.06	-0.01	0.54	0.57	0.23	0.12	0.12	0.11	0.11	0.00	-0.10	0.08	0.00	0.09	0.05	0.15	0.04	0.01	0.15	0.04	0.05	0.02	0.03	0.04	0.00	0.10	0.07	0.08	0.10	-0.07	-0.05	1.00	0.99	0.98	-0.13	-0.16	-0.17
temp_change	-0.13	0.00	0.01	0.00	-0.09	-0.19	-0.10	0.38	-0.18	0.06	0.03	-0.19	-0.10	0.01	0.53	0.60	0.16	0.18	0.09	0.19	0.05	-0.04	-0.10	0.06	-0.02	0.07	0.04	0.11	0.09	0.00	0.12	0.02	0.02	0.01	0.03	0.04	0.02	0.08	0.01	0.07	0.08	-0.08	-0.06	0.99	1.00	0.99	-0.10	-0.12	-0.12
annual_mean_prec	-0.14	0.00	-0.05	0.02	-0.13	-0.20	-0.10	0.36	-0.19	0.10	0.01	-0.18	-0.15	0.04	0.51	0.63	0.14	0.22	0.07	0.27	0.04	-0.05	-0.08	0.07	-0.01	0.06	0.04	0.10	0.12	0.01	0.11	0.02	0.02	0.00	0.03	0.03	0.01	0.06	0.00	0.06	0.08	-0.07	-0.05	0.98	0.99	1.00	-0.09	-0.10	-0.09
rasio_40pers_ekon_rendah_rt	0.13	0.32	0.06	-0.06	-0.11	0.17	-0.01	0.05	-0.51	0.28	-0.19	-0.12	-0.03	0.12	0.17	0.09	-0.44	0.37	-0.24	0.06	-0.50	-0.32	-0.20	-0.58	-0.63	-0.26	0.06	-0.41	0.22	0.06	-0.14	0.02	0.07	0.04	-0.07	0.03	0.02	0.03	-0.60	0.25	0.08	0.02	0.00	-0.13	-0.10	-0.09	1.00	0.98	0.10
rasio_40pers_ekon_rendah_indv	0.09	0.28	-0.06	0.01	-0.15	0.10	-0.03	0.01	-0.47	0.26	-0.20	-0.09	-0.07	0.13	0.11	0.12	-0.44	0.37	-0.22	0.15	-0.53	-0.32	-0.17	-0.53	-0.58	-0.27	0.00	-0.42	0.21	0.03	-0.17	0.01	0.04	0.03	-0.07	0.01	0.03	-0.01	-0.61	0.18	0.01	0.00	-0.02	-0.16	-0.12	-0.10	0.98	1.00	0.19
prec_change	0.07	0.13	-0.46	0.08	-0.19	-0.11	-0.20	-0.20	0.04	0.08	-0.08	0.07	-0.06	0.04	-0.27	0.08	-0.22	0.13	0.07	0.27	-0.32	-0.05	0.00	-0.02	0.03	-0.12	-0.05	-0.21	0.13	-0.04	-0.19	-0.12	0.09	0.01	0.02	0.01	0.10	-0.30	-0.17	-0.31	-0.27	-0.11	-0.14	-0.17	-0.12	-0.09	0.10	0.19	1.00

Code

# Set a threshold value for correlation
threshold <- 0.8

# Find the indices of the variables that are highly correlated according to the specified threshold in the correlation matrix 'cor_matrix.'
# This will be used to remove the highly correlated variables from 'df_pre_pca.'
highly_correlated <- findCorrelation(cor(df_pre_pca), cutoff = threshold, names = FALSE)

# If you also need the names of the highly correlated variables, you can extract them using the indices.
highly_correlated_names <- colnames(cor(df_pre_pca))[highly_correlated]


# # Remove the columns from 'df_pre_pca' that correspond to the indices of the highly correlated variables.
# df_pre_pca <- df_pre_pca |> dplyr::select(-highly_correlated_names[[1]])
# Create a data frame from highly_correlated_names and threshold
highly_correlated_df <- data.frame(
  Predictor = highly_correlated_names
 # Threshold = threshold
)

# Create a gt table
highly_correlated_df|>
  gt()|>
  tab_header(
    title = "Highly Correlated Predictors",
    subtitle = paste("Predictors with correlation above", threshold)
  )|>
  cols_label(
    Predictor = "Predictor Name"
   # Threshold = "Correlation Threshold"
  )

Highly Correlated Predictors
Predictors with correlation above 0.8
Predictor Name
total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik
percentage_of_forested_area_in_the_sub_district
rasio_40pers_ekon_rendah_rt
distance_to_forest
annual_mean_temp
annual_mean_prec
jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018

4 Exploratory data analysis (EDA)

Visualize the data and examine any patterns, distributions, or outliers. In Principal Component Analysis (PCA), you want to reduce the dimensionality of your dataset to uncover patterns and make visualization easier. However, if some variables (columns) have constant or near-constant values across the observations, they can’t contribute to explaining the variability in your data. Such columns are advised to be removed before performing PCA.

Code

# Pivot the 'scaled_df_complete_temp' dataframe to long format
# Exclude certain columns from being pivoted and specify the new column names for 'variable' and 'value'
df_long <- scaled_df_complete_temp |> 
  dplyr::select(1:9) |> bind_cols(df_pre_pca) |> 
  tidyr::pivot_longer(
    cols = -c(idkec_dum, sumber, kdprov, nmprov, nmkab, nmkec, periode, kdkab, kdkec),
    names_to = "variable",
    values_to = "value"
  )

# Select only the 'variable' and 'value' columns from the long-form data
# Remove unwanted columns and group by 'variable' to prepare for summarization
gt_tab <- df_long |>
  dplyr::select(-c(idkec_dum, sumber, kdprov, nmprov, nmkab, nmkec, periode, kdkab, kdkec)) |>
  group_by(variable) 

# Calculate summary statistics for each group (each 'variable')
# Also, keep the original 'value' data in a list column called 'value_data'
# Use '.groups = "drop"' to return a regular dataframe rather than a grouped one
gt_stat <- gt_tab |> 
  summarise(
    min = min(value, na.rm = TRUE),
    max = max(value, na.rm = TRUE),
    median = median(value, na.rm = TRUE),
    #mean = mean(value, na.rm = TRUE),
    #sd = sd(value, na.rm = TRUE),
    value_data = list(value),
    .groups = "drop"
  )

# Create a GT table with a density plot column
# The density plot is generated from the 'value_data' list column
# Customize the appearance of the density plot and format the number columns
gt_stat |>
  gt::gt() |> 
  gtExtras::gt_plt_dist(
    value_data,
    type = "density",
    line_color = "blue",
    fill_color = "red"
  ) |> gt::fmt_number(columns = min:median, decimals = 1) |> 
  cols_label(
    variable = "Predictors",
    min = "Minimum",
    max = "Maximum",
    median = "Median",
    value_data = "Density"
  ) 

Predictors	Minimum	Maximum	Median	Density
annual_mean_prec	−7.8	0.3	0.1
annual_mean_temp	−7.8	0.2	0.2
arable_land_percent	−4.5	0.6	0.3
aridity_index	−4.3	1.5	0.3
banyak_kejadian_banjir_2018_2019	−1.1	1.5	0.5
banyak_kejadian_banjir_bandang_2018_2019	−0.3	4.0	−0.3
banyak_kejadian_kebakaran_hutan_dan_lahan_2018_2019	−0.3	4.1	−0.3
banyak_kejadian_kekeringan_lahan_2018_2019	−0.4	3.3	−0.4
banyak_kejadian_tanah_longsor_2018_2019	−0.8	1.8	−0.8
buffer_to_500m_irigated_land	−0.7	2.1	−0.7
distance_to_burned_area	−2.5	3.6	−0.1
distance_to_commodity_processing_factory	−3.4	2.2	0.2
distance_to_deforestation	−2.4	2.2	0.0
distance_to_forest	−4.4	2.0	0.1
distance_to_plantation	−3.1	2.9	0.1
distance_to_plantation_concession	−4.4	0.6	0.3
distance_to_river	−1.9	4.6	−0.1
distance_to_road	−3.7	2.9	−0.1
erosion_risk_t_ha_1_yr_1	−8.3	1.1	0.2
indeks_bahaya_banjir	−2.0	1.2	0.3
indeks_bahaya_longsor	−1.5	1.1	0.4
jumlah_sistem_peringatan_dini_bencana_alam	−2.7	2.8	0.0
jumlah_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	−0.9	1.8	−0.9
korban_jiwa_banjir_2018_2019	−0.2	5.4	−0.2
korban_jiwa_banjir_bandang_2018_2019	−0.1	8.7	−0.1
korban_jiwa_kekeringan_lahan_2018_2019	−0.1	17.6	−0.1
korban_jiwa_tanah_longsor_2018_2019	−0.1	10.1	−0.1
percentage_deforestation_area_size	−0.9	2.6	−0.3
percentage_of_agricultural_area_small_holder_in_the_village	−3.2	1.0	0.3
percentage_of_forested_area_in_the_sub_district	−1.1	1.6	0.0
percentage_of_plantation_area_per_sub_district	−1.8	2.2	0.0
percentage_of_shrubland_in_the_sub_district	−0.2	6.6	−0.2
percentage_of_water_area_compared_to_sub_district_area	−0.2	11.6	−0.2
persentase_sistem_peringatan_dini_bencana_alam	−2.7	3.2	0.0
prec_change	−2.8	2.0	0.1
rasio_40pers_ekon_rendah_indv	−4.3	2.4	0.1
rasio_40pers_ekon_rendah_rt	−4.1	2.3	0.1
rasio_elektrifikasi	−8.7	0.5	0.4
rasio_embung_di_kecamatan	−1.2	1.4	0.6
rasio_faskes_1	−13.8	2.2	0.1
rasio_minimarket_swalayan	−1.4	0.9	0.6
rasio_pasar	−0.5	16.8	−0.1
rasio_pasar_desa_pasar_hewan_pelelangan_ikan_pelelangan_hasil_pertanian_dll	−0.8	1.6	−0.8
rasio_pt	−0.5	2.2	−0.5
rasio_rs	−0.5	2.4	−0.5
rasio_sekolah_tinggi_sma_sederajat	−2.0	2.8	−0.1
rasio_warga_penderita_gizi_buruk_marasmus_dan_kwashiorkor_pada_tahun_2018	−0.9	1.4	−0.9
temp_change	−7.8	0.4	0.1
total_kk_berdasarkan_pengguna_dan_non_pengguna_listrik	−2.9	2.9	0.1

Code

## Boxplot
# Histograms
# boxplot(df_pre_pca)

4.1 Density plots

5 PCA Analysis

Code

# Perform PCA
pca_result <- prcomp(df_pre_pca)

Code

# Assuming pca_result is your prcomp object
pca_summary <- summary(pca_result)$importance |> round(digits = 2)

# Convert to tibble and remove row names
pca_summary_tibble <- tibble::rownames_to_column(as.data.frame(pca_summary), var = "Components")

# Create gt table
pca_summary_tibble|>  
  gt()|>
  tab_header(
    title = "Principal Component Analysis Summary",
    subtitle = "Importance of components") |> 
    opt_align_table_header(align = "left")

Principal Component Analysis Summary
Importance of components
Components	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8	PC9	PC10	PC11	PC12	PC13	PC14	PC15	PC16	PC17	PC18	PC19	PC20	PC21	PC22	PC23	PC24	PC25	PC26	PC27	PC28	PC29	PC30	PC31	PC32	PC33	PC34	PC35	PC36	PC37	PC38	PC39	PC40	PC41	PC42	PC43	PC44	PC45	PC46	PC47	PC48	PC49
Standard deviation	2.83	2.07	2.01	1.75	1.60	1.44	1.34	1.29	1.16	1.11	1.08	1.06	1.03	1.02	0.99	0.96	0.94	0.90	0.89	0.88	0.86	0.85	0.83	0.78	0.75	0.74	0.70	0.67	0.66	0.61	0.61	0.59	0.56	0.53	0.50	0.49	0.47	0.42	0.40	0.36	0.33	0.3	0.26	0.23	0.16	0.1	0.05	0.02	0
Proportion of Variance	0.17	0.09	0.08	0.06	0.05	0.04	0.04	0.03	0.03	0.03	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.02	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.0	0.00	0.00	0.00	0.0	0.00	0.00	0
Cumulative Proportion	0.17	0.26	0.34	0.40	0.46	0.50	0.54	0.57	0.60	0.63	0.65	0.67	0.70	0.72	0.74	0.76	0.77	0.79	0.81	0.82	0.84	0.85	0.87	0.88	0.89	0.90	0.92	0.92	0.93	0.94	0.95	0.96	0.96	0.97	0.97	0.98	0.98	0.99	0.99	0.99	0.99	1.0	1.00	1.00	1.00	1.0	1.00	1.00	1

5.1 The Scree Plot

A scree plot visualizes the proportion of variance explained by each PC. The first few PCs are the main contributors, while the rest have minimal influence.

Code

# Visualize the PCA result using a scree plot to see the variance explained by each principal component
plot(pca_result, type = "l", main = "Scree Plot")

5.2 A Look at Loadings

Loadings in PCA reveal how original variables influence each Principal Component. High absolute values indicate strong influence, while the sign indicates the direction. Understanding these can uncover underlying themes, such as climate factors.

5.2.0.1 The importance of the factors for each principal component

Code

# Extract the loadings for the desired number of principal components
num_pc <- 5
loadings <- pca_result$rotation[, 1:num_pc]

# Function to plot ordered loadings
plot_ordered_loadings <- function(loadings, pc_num) {
  ordered_indices <- order(-abs(loadings[, pc_num]), decreasing = TRUE)
  
  # Determine the colours based on the sign of the values
  bar_colours <- ifelse(loadings[ordered_indices, pc_num] < 0, "red", "blue")
  
  barplot(abs(loadings[ordered_indices, pc_num]), horiz = TRUE,
          main = paste("Loadings for PC", pc_num),
          names.arg = rownames(loadings)[ordered_indices],
          las = 1, cex.names = 0.7, xlim = c(0, 0.5), col = bar_colours)
}

# Set up the plotting area with adjusted margins
par(mar = c(5, 25, 4, 2))

# Loop over each principal component and plot
for (i in 1:num_pc) {
  plot_ordered_loadings(loadings, i)
}

To identify the factors that are consistently least influential across the first three principal components, we can look at the absolute values of the loadings. Factors with small absolute loadings are less influential. Knowledge of the specific field aids in interpreting PCs. Principal Components can be complex and may resist straightforward interpretation.

6 Classifying Data with K-Means Clustering

6.0.1 Step 1: Selecting the Principal Components

Start by using the top five Principal Components from PCA, which capture the core variances and correlations in your data.

Code

# Extract the first five principal components
selected_components <- pca_result$x[, 1:5]

6.0.2 Step 2: Determine the Number of Clusters

Select the optimal number of clusters (k) using methods like the Elbow Method or Silhouette Analysis.

6.0.2.1 Elbow Method

The Elbow Method involves running k-means clustering for a range of \(k\) values and plotting the total within-cluster sum of squares. The “elbow” of the plot represents an optimal value for \(k\) (a balance between precision and computational cost).

Code

# Compute total within-cluster sum of squares for different k values
set.seed(45)
wss <- sapply(1:10, function(k) {
  kmeans(selected_components, centers = k)$tot.withinss
})

# Plot the total within-cluster sum of squares
plot(1:10, wss, type = "b", xlab = "Number of Clusters", ylab = "Total Within-Cluster Sum of Squares",
     main = "Elbow Method")

based on the numbers, we might consider the point where the decrease starts to slow down, which could be around \(k\)= 4 or \(k\)=5.

6.0.2.2 Silhouette Analysis

Silhouette Analysis measures how similar an object is to its own cluster compared to other clusters. The silhouette score ranges from -1 to 1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters.

Code

library(cluster)

# Compute silhouette scores for different k values
set.seed(45)
silhouette_scores <- sapply(2:10, function(k) {
  cluster_result <- kmeans(selected_components, centers = k)
  silhouette_avg <- mean(silhouette(cluster_result$cluster, dist(selected_components))[, "sil_width"])
  silhouette_avg
})

# Plot the silhouette scores
plot(2:10, silhouette_scores, type = "b", xlab = "Number of Clusters", ylab = "Average Silhouette Width",
     main = "Silhouette Analysis")

The maximum silhouette score corresponds to 5 clusters (since the first value represents \(k\)=2)

6.0.3 Step 3: Applying K-Means Algorithm

Utilize the k-means algorithm to divide the data into k clusters, focusing on the first three PCs. In R, this can be done with:

Code

# Choose the number of clusters
k <- 5

# Perform k-means clustering
set.seed(45)
kmeans_result <- kmeans(selected_components, centers = k)

6.0.4 Step 4: Interpret the Clusters

Investigate each cluster to understand the common traits within them. Interpretation requires a blend of data analysis and domain-specific knowledge.

Code

library(ggplot2)

# Create a data frame for plotting
plot_data <- data.frame(selected_components, cluster = as.factor(kmeans_result$cluster))

# Plot the first two principal components and color by cluster
ggplot(plot_data, aes(x = PC1, y = PC2, color = cluster)) +
  geom_point() +
  labs(title = "K-means Clustering on First Two Principal Components") +
  theme_minimal()

Code

# Plot the first two principal components and color by cluster
ggplot(plot_data, aes(x = PC1, y = PC3, color = cluster)) +
  geom_point() +
  labs(title = "K-means Clustering on First and Third Principal Components") +
  theme_minimal()

An interactive 3D scatter plot below shows the first three principal components, colored by cluster. We can rotate the plot to view it from different angles, and you can hover over the points to see additional information.

Code

# Load the plotly package
library(plotly)
names_kab_kec<- scaled_df_complete_temp |> 
  select(c(nmkab, nmkec))

# Create a data frame for plotting
plot_data <- data.frame(selected_components, cluster = as.factor(kmeans_result$cluster)) |> bind_cols(names_kab_kec)

# Create the 3D scatter plot
plot_3d <- plot_ly(
  data = plot_data,
  x = ~ PC1,
  y = ~ PC2,
  z = ~ PC3,
  color = ~ cluster,
  type = "scatter3d",
  text = ~ paste("Kab./Kota:", nmkab, "<br>Kecamatan:", nmkec),
  mode = "markers"
) 
# Show the plot
plot_3d

6.0.5 Step 5: Visualise the clusters into a map

Code

library(terra)
library(sf)
# Read the shapefile
desa <-
  st_read("data/INDO_DESA_2019/INDO_DESA_2019.shp", quiet = TRUE)

# Filter based on the 'kdprov' attribute
desa_sulsel <- desa |> filter(kdprov %in% 73)
desa_sulsel <- desa_sulsel |> dplyr::select(-c("kddesa", "iddesa"))
desa_sulsel_id_kec <-
  desa_sulsel |> select(nmkab, nmkec, kdprov, kdkab, kdkec) |>
  mutate(idkec_dum = paste0(kdprov, kdkab, kdkec, "a"))
rm(desa)

# add the cluster attribute to the desa_sulsel object
cluster_data <-
  scaled_df_complete_temp |> select(-c(nmkab, nmkec , nmprov,  sumber, kdprov, kdkab, kdkec)) |>
  dplyr::select(1:9) |> bind_cols(tibble (cluster = kmeans_result$cluster))

clusters_sulsel <-
  desa_sulsel_id_kec |> left_join(cluster_data, by = "idkec_dum")

# Write the sf object to a shapefile
st_write(
  clusters_sulsel,
  "output/tipologi_5_kelas.shp",
  append = TRUE,
  quiet = TRUE
)

# # Plot the SpatVector object, using the 'cluster' attribute for the fill color
# plot(desa_sulsel, "cluster", col=c("#E69F00", "#CC79A7", "#009E73", "#F0E442", "#0072B2"), lwd=0.1) # Assuming we have 5 clusters

library(leaflet)
# Create a color palette for the 'cluster' variable
pal <-
  colorFactor(palette = "Set1", domain = clusters_sulsel$cluster)

# Constructing the label string first
clusters_sulsel$label_content <- with(
  clusters_sulsel,
  paste0(
    "<strong>Kabupaten:</strong> ",
    nmkab,
    "<br>",
    "<strong>Kecamatan:</strong> ",
    nmkec,
    "<br>",
    "<strong>Cluster:</strong> ",
    cluster
  )
) |> lapply(htmltools::HTML)


# Create the leaflet map with HTML-rendered labels
leaflet(clusters_sulsel) |>
  addProviderTiles(providers$OpenStreetMap) |>
  addPolygons(
    fillColor = ~ pal(cluster),
    weight = 0.5,
    opacity = 1,
    color = "white",
    dashArray = "3",
    fillOpacity = 0.7,
    highlight = highlightOptions(
      weight = 5,
      color = "#666",
      dashArray = "",
      fillOpacity = 0.7,
      bringToFront = TRUE
    ),
    label = ~ label_content,
    labelOptions = labelOptions(noHide = FALSE,
                                direction = 'auto')
  ) |>
  addLegend(pal = pal,
            values = ~ cluster,
            title = "Cluster")

7 Warning

The analysis was conducted without in-depth knowledge of the region, so the results should be interpreted cautiously.